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Block #2,645,073

TWNLength 12β˜…β˜…β˜…β˜…β˜†

Bi-Twin Chain Β· Discovered 5/2/2018, 6:34:55 PM Β· Difficulty 11.7237 Β· 4,193,289 confirmations

TWN
Bi-Twin Chain

Interleaved pairs of primes that differ by 2, forming twin prime pairs at each level.

Block Header
Block Hash
208432e2d76efb42c0814c451f80e995a36471cde14bef07f5a3429d597742bf
View on Chainz β†—

Height

#2,645,073

Difficulty

11.723651

Transactions

2

Size

575 B

Version

2

Bits

0bb9412e

Nonce

1,639,293,328

Timestamp

5/2/2018, 6:34:55 PM

Confirmations

4,193,289

Mined by

⛏️ P2SHAR59CMsgjDdHAr5UPBKixY5CSo9EEs2G9Y

Merkle Root

99ba3b2f516cc7cda16f8a8e54da153db9080970cea86837187eb46b1e95362a
Transactions (2)
Coinbase99d1956393bef6…70f5e24bb96391
1 in β†’ 1 out7.2700 XPM110 B
AR59CMsg…9EEs2G9Y
2687a5423c3162…644999e42a3265
2 in β†’ 2 out25.0103 XPM374 B
Ac8YpeEA…Wee7cykqAe2sr8NG…pMah4pBZ
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) β€” it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

9.978 Γ— 10⁹⁷(98-digit number)
99783898963680758452…70813116263936880639
Discovered Prime Numbers
Lower: 2^k Γ— origin βˆ’ 1 | Upper: 2^k Γ— origin + 1

These are the actual prime numbers discovered by this block, computed using the verified Primecoin formula. Each number has been independently confirmed to pass the Fermat primality test. Use the FactorDB links to verify any number independently.

Level 0 β€” Twin Prime Pair (origin Β± 1)
origin βˆ’ 1
9.978 Γ— 10⁹⁷(98-digit number)
99783898963680758452…70813116263936880639
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
9.978 Γ— 10⁹⁷(98-digit number)
99783898963680758452…70813116263936880641
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: origin + 1 βˆ’ origin βˆ’ 1 = 2 (twin primes βœ“)
Level 1 β€” Twin Prime Pair (2^1 Γ— origin Β± 1)
2^1 Γ— origin βˆ’ 1
1.995 Γ— 10⁹⁸(99-digit number)
19956779792736151690…41626232527873761279
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.995 Γ— 10⁹⁸(99-digit number)
19956779792736151690…41626232527873761281
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^1 Γ— origin + 1 βˆ’ 2^1 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 2 β€” Twin Prime Pair (2^2 Γ— origin Β± 1)
2^2 Γ— origin βˆ’ 1
3.991 Γ— 10⁹⁸(99-digit number)
39913559585472303381…83252465055747522559
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.991 Γ— 10⁹⁸(99-digit number)
39913559585472303381…83252465055747522561
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^2 Γ— origin + 1 βˆ’ 2^2 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 3 β€” Twin Prime Pair (2^3 Γ— origin Β± 1)
2^3 Γ— origin βˆ’ 1
7.982 Γ— 10⁹⁸(99-digit number)
79827119170944606762…66504930111495045119
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
7.982 Γ— 10⁹⁸(99-digit number)
79827119170944606762…66504930111495045121
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^3 Γ— origin + 1 βˆ’ 2^3 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 4 β€” Twin Prime Pair (2^4 Γ— origin Β± 1)
2^4 Γ— origin βˆ’ 1
1.596 Γ— 10⁹⁹(100-digit number)
15965423834188921352…33009860222990090239
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.596 Γ— 10⁹⁹(100-digit number)
15965423834188921352…33009860222990090241
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 5 β€” Twin Prime Pair (2^5 Γ— origin Β± 1)
2^5 Γ— origin βˆ’ 1
3.193 Γ— 10⁹⁹(100-digit number)
31930847668377842704…66019720445980180479
Verify on FactorDB β†—Wolfram Alpha β†—
2^5 Γ— origin + 1
3.193 Γ— 10⁹⁹(100-digit number)
31930847668377842704…66019720445980180481
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^5 Γ— origin + 1 βˆ’ 2^5 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 12 consecutive prime numbers forming a Bi-Twin Chain. The prime chain origin β€” the large number shown above β€” anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

β˜…β˜…β˜…β˜…β˜†
Rarity
ExceptionalChain length 12

Around 1 in 10,000 blocks. A significant mathematical achievement.

How Primecoin's Proof-of-Work Constructs These Primes

Primecoin stores a value called the prime chain origin in each block. The miner found a large integer such that when divided by a primorial (the product of small primes: 2 Γ— 3 Γ— 5 Γ— 7 Γ— …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial β€” that divisibility is part of the proof.

Prime Chain Origin = First Prime Γ— Primorial (2Β·3Β·5Β·7Β·11·…)
Source: Primecoin prime.cpp β€” CheckPrimeProofOfWork()

This is why the origin has many small prime factors β€” those factors are the primorial divisor. The chain then extends from the first prime using the TWN formula:

TWN: twin pairs (p, p+2) where p = origin/primorial βˆ’ 1 and p+2 = origin/primorial + 1
Cross-reference on Chainz Explorer
Circulating Supply:57,951,164 XPMΒ·at block #6,838,361 Β· updates every 60s
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