Block #2,557,262

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 3/9/2018, 4:22:30 PM · Difficulty 10.9913 · 4,276,711 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

2fa3b00fce7deb5cfe788f52de2629be38697cc0832d4bc1a931f4b2a2b412b9

View on Chainz ↗

Height

#2,557,262

Difficulty

10.991316

Transactions

Size

845 B

Version

Bits

0afdc6e3

Nonce

1,305,070,750

Timestamp

3/9/2018, 4:22:30 PM

Confirmations

4,276,711

Mined by

⛏️ P2SHAXaGYGmktWgywFxZN4B2yXPmaMsgA1X7tg

Merkle Root

1ff03e4f60dc6b8421dd201ef4c6699f9864eec3b1e3f54bdd029891b8a9fb7e

Transactions (3)

Coinbase545aebd849d6b5…66ad6ace98b629

1 in → 1 out8.2800 XPM109 B

AXaGYGmk…sgA1X7tg

c74192f1d668c8…ab37f6b1fbed14

2 in → 2 out16.5300 XPM306 B

AXDbMD6L…MfxE69sJ Ae5yaGzT…iYSKtYox

309eedb6c95074…81861e490b2378

2 in → 2 out14.7900 XPM339 B

ATjRX3ay…ivqZbv7Y AakBtsj3…644etSjs

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.

3.465 × 10⁹⁷(98-digit number)

34657429959465188761…99408069541129215999

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

3.465 × 10⁹⁷(98-digit number)

34657429959465188761…99408069541129215999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.465 × 10⁹⁷(98-digit number)

34657429959465188761…99408069541129216001

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

6.931 × 10⁹⁷(98-digit number)

69314859918930377523…98816139082258431999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.931 × 10⁹⁷(98-digit number)

69314859918930377523…98816139082258432001

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

1.386 × 10⁹⁸(99-digit number)

13862971983786075504…97632278164516863999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.386 × 10⁹⁸(99-digit number)

13862971983786075504…97632278164516864001

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

2.772 × 10⁹⁸(99-digit number)

27725943967572151009…95264556329033727999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.772 × 10⁹⁸(99-digit number)

27725943967572151009…95264556329033728001

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

5.545 × 10⁹⁸(99-digit number)

55451887935144302018…90529112658067455999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.545 × 10⁹⁸(99-digit number)

55451887935144302018…90529112658067456001

Verify on FactorDB ↗Wolfram Alpha ↗

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

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

1.109 × 10⁹⁹(100-digit number)

11090377587028860403…81058225316134911999

Verify on FactorDB ↗Wolfram Alpha ↗

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 — 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

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 × 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 #2,557,262

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