Block #2,479,054

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/18/2018, 4:33:59 PM · Difficulty 10.9658 · 4,360,995 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

022649dc82c1ef015a02fd8dc24e716316acac4145d38c0a1b2ca099778433d8

View on Chainz ↗

Height

#2,479,054

Difficulty

10.965806

Transactions

Size

392 B

Version

Bits

0af73f15

Nonce

1,144,907,715

Timestamp

1/18/2018, 4:33:59 PM

Confirmations

4,360,995

Mined by

⛏️ P2SHAbMdFE5qjqBEREuTpaZc4WsSXhXZJkG3NT

Merkle Root

ba413781869fd515102313dd1a2759aa90db9456573f5fd10ab2925f3f9ce7f6

Transactions (2)

Coinbase1117812a972921…20e7e2e72294b4

1 in → 1 out8.3100 XPM109 B

AbMdFE5q…XZJkG3NT

66b077d209fa3e…38df09f6e508a9

1 in → 2 out8.3000 XPM193 B

AN24acsN…j8WmedDv ATDSXsmP…JYSc3iUt

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.

4.858 × 10⁹⁴(95-digit number)

48580172045227738141…21275293059272895999

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

4.858 × 10⁹⁴(95-digit number)

48580172045227738141…21275293059272895999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.858 × 10⁹⁴(95-digit number)

48580172045227738141…21275293059272896001

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

9.716 × 10⁹⁴(95-digit number)

97160344090455476282…42550586118545791999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.716 × 10⁹⁴(95-digit number)

97160344090455476282…42550586118545792001

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

1.943 × 10⁹⁵(96-digit number)

19432068818091095256…85101172237091583999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.943 × 10⁹⁵(96-digit number)

19432068818091095256…85101172237091584001

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

3.886 × 10⁹⁵(96-digit number)

38864137636182190512…70202344474183167999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.886 × 10⁹⁵(96-digit number)

38864137636182190512…70202344474183168001

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

7.772 × 10⁹⁵(96-digit number)

77728275272364381025…40404688948366335999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.772 × 10⁹⁵(96-digit number)

77728275272364381025…40404688948366336001

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 #2,479,054

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