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Block #2,077,196

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 4/19/2017, 5:18:21 AM Β· Difficulty 10.8484 Β· 4,759,470 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
0d4c43cde5cc8e3cef444ccaacf69331a756560c09011074c0e242d4a0402c99
View on Chainz β†—

Height

#2,077,196

Difficulty

10.848377

Transactions

1

Size

209 B

Version

2

Bits

0ad92f37

Nonce

192,536,938

Timestamp

4/19/2017, 5:18:21 AM

Confirmations

4,759,470

Mined by

⛏️ jhPrimeminerAM6GYpjwZFjhLNzHZAfmRp8jwiaw86QDtR

Merkle Root

260414879c8b08c123d706f7233ade4eea701a9c3ec2afae0b9f5e9211c4f22f
Transactions (1)
Coinbase260414879c8b08…9f5e9211c4f22f
1 in β†’ 1 out8.4800 XPM118 B
AM6GYpjw…aw86QDtR
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.

1.772 Γ— 10⁹⁸(99-digit number)
17727303017565059723…68333834448499752959
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
1.772 Γ— 10⁹⁸(99-digit number)
17727303017565059723…68333834448499752959
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.772 Γ— 10⁹⁸(99-digit number)
17727303017565059723…68333834448499752961
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
3.545 Γ— 10⁹⁸(99-digit number)
35454606035130119447…36667668896999505919
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.545 Γ— 10⁹⁸(99-digit number)
35454606035130119447…36667668896999505921
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
7.090 Γ— 10⁹⁸(99-digit number)
70909212070260238894…73335337793999011839
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
7.090 Γ— 10⁹⁸(99-digit number)
70909212070260238894…73335337793999011841
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
1.418 Γ— 10⁹⁹(100-digit number)
14181842414052047778…46670675587998023679
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.418 Γ— 10⁹⁹(100-digit number)
14181842414052047778…46670675587998023681
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
2.836 Γ— 10⁹⁹(100-digit number)
28363684828104095557…93341351175996047359
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.836 Γ— 10⁹⁹(100-digit number)
28363684828104095557…93341351175996047361
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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:57,937,606 XPMΒ·at block #6,836,665 Β· updates every 60s
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