Block #1,556,177

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/24/2016, 6:31:09 PM · Difficulty 10.6759 · 5,257,841 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

04b69d57367aedef6abccb49aec0bebd390c2f913f831415aad2f3e0649b5859

View on Chainz ↗

Height

#1,556,177

Difficulty

10.675871

Transactions

Size

527 B

Version

Bits

0aad05e0

Nonce

936,613,113

Timestamp

4/24/2016, 6:31:09 PM

Confirmations

5,257,841

Mined by

⛏️ P2SHALWFNWa6n1JsjYx7VzLX3g44dtwDyKbLkX

Merkle Root

34075b85d0b9607570d82c93343e99b8721efe1d74aca965d4f16a6de379cfc2

Transactions (2)

Coinbase4e88c446e726dc…09066ae9e4f5f2

1 in → 1 out8.7700 XPM110 B

ALWFNWa6…wDyKbLkX

fc2e0ae256dd52…4cd8621d817b10

1 in → 6 out8.7800 XPM327 B

AeBwvm57…kL6E7ayF ALqEZWdP…6VPV6ooe AWVdqMHf…3TnrQBYd AVvA9Gzu…7fxjvGRS ALKgih3X…yaVE74WK

Prime Chain Origin

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

1.074 × 10⁹⁴(95-digit number)

10746616135566469710…19649103417238050919

Discovered Prime Numbers

Lower: 2^k × origin − 1 | Upper: 2^k × 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 — Twin Prime Pair (origin ± 1)

origin − 1

1.074 × 10⁹⁴(95-digit number)

10746616135566469710…19649103417238050919

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.074 × 10⁹⁴(95-digit number)

10746616135566469710…19649103417238050921

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: origin + 1 − origin − 1 = 2 (twin primes ✓)

Level 1 — Twin Prime Pair (2^1 × origin ± 1)

2^1 × origin − 1

2.149 × 10⁹⁴(95-digit number)

21493232271132939421…39298206834476101839

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.149 × 10⁹⁴(95-digit number)

21493232271132939421…39298206834476101841

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^1 × origin + 1 − 2^1 × origin − 1 = 2 (twin primes ✓)

Level 2 — Twin Prime Pair (2^2 × origin ± 1)

2^2 × origin − 1

4.298 × 10⁹⁴(95-digit number)

42986464542265878843…78596413668952203679

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.298 × 10⁹⁴(95-digit number)

42986464542265878843…78596413668952203681

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^2 × origin + 1 − 2^2 × origin − 1 = 2 (twin primes ✓)

Level 3 — Twin Prime Pair (2^3 × origin ± 1)

2^3 × origin − 1

8.597 × 10⁹⁴(95-digit number)

85972929084531757686…57192827337904407359

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.597 × 10⁹⁴(95-digit number)

85972929084531757686…57192827337904407361

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^3 × origin + 1 − 2^3 × origin − 1 = 2 (twin primes ✓)

Level 4 — Twin Prime Pair (2^4 × origin ± 1)

2^4 × origin − 1

1.719 × 10⁹⁵(96-digit number)

17194585816906351537…14385654675808814719

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.719 × 10⁹⁵(96-digit number)

17194585816906351537…14385654675808814721

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

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 — the large number shown above — anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

★★☆☆☆

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 × 3 × 5 × 7 × …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial — that divisibility is part of the proof.

Prime Chain Origin = First Prime × Primorial (2·3·5·7·11·…)

Source: Primecoin prime.cpp — CheckPrimeProofOfWork()

This is why the origin has many small prime factors — 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 − 1 and p+2 = origin/primorial + 1

Cross-reference on Chainz Explorer

Block #1,556,177

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