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Block #2,164,078

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 6/17/2017, 5:06:13 AM Β· Difficulty 10.8994 Β· 4,663,155 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
95bf54bc7d95d90b20efdbd7bc18faf619c6bca2e9b8ef5bc5b7767d42890ac6
View on Chainz β†—

Height

#2,164,078

Difficulty

10.899351

Transactions

2

Size

4.72 KB

Version

2

Bits

0ae63bda

Nonce

1,606,601,293

Timestamp

6/17/2017, 5:06:13 AM

Confirmations

4,663,155

Mined by

⛏️ P2SHAUPa2DA6ARoWr1fLvBxNa2ifwn27PcjxuP

Merkle Root

6c35019e3dac334bff9e8a8f152ce2a0806e29f2374341445c8e698985fe1906
Transactions (2)
Coinbase6272f44b8d0839…cba876a5d327c3
1 in β†’ 1 out8.4800 XPM109 B
AUPa2DA6…27PcjxuP
0968356dc4454b…c2402dcdf3f68b
31 in β†’ 1 out809.8844 XPM4.52 KB
AGxk1TD6…rMWoF8Ha
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.

1.319 Γ— 10⁹⁷(98-digit number)
13199350628414234935…21158949991044751359
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
1.319 Γ— 10⁹⁷(98-digit number)
13199350628414234935…21158949991044751359
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.319 Γ— 10⁹⁷(98-digit number)
13199350628414234935…21158949991044751361
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
2.639 Γ— 10⁹⁷(98-digit number)
26398701256828469870…42317899982089502719
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.639 Γ— 10⁹⁷(98-digit number)
26398701256828469870…42317899982089502721
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
5.279 Γ— 10⁹⁷(98-digit number)
52797402513656939741…84635799964179005439
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
5.279 Γ— 10⁹⁷(98-digit number)
52797402513656939741…84635799964179005441
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
1.055 Γ— 10⁹⁸(99-digit number)
10559480502731387948…69271599928358010879
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.055 Γ— 10⁹⁸(99-digit number)
10559480502731387948…69271599928358010881
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
2.111 Γ— 10⁹⁸(99-digit number)
21118961005462775896…38543199856716021759
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.111 Γ— 10⁹⁸(99-digit number)
21118961005462775896…38543199856716021761
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
4.223 Γ— 10⁹⁸(99-digit number)
42237922010925551793…77086399713432043519
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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:57,861,964 XPMΒ·at block #6,827,232 Β· updates every 60s
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