Block #619,735

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 7/6/2014, 12:50:42 PM · Difficulty 10.9483 · 6,191,252 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d8bc21b9d60efc16573692181cf8a1dfb91f0a2b86bc3e426b7bfec92addae16

View on Chainz ↗

Height

#619,735

Difficulty

10.948275

Transactions

Size

661 B

Version

Bits

0af2c22b

Nonce

15,745,681

Timestamp

7/6/2014, 12:50:42 PM

Confirmations

6,191,252

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

305f762f576b1880764d068682c30eb514ac001933e36d87187f6ee2fb7e6d5d

Transactions (3)

Coinbase42ae96e0e79bac…222c6d0dc6c1ef

1 in → 1 out8.3500 XPM116 B

ANSXnLY2…Sd25TjkD

30304390977544…9e5ea7f0024da9

1 in → 2 out7.0175 XPM227 B

AHtxE5yG…5HVgag4v AZm6Ys13…SSngZLR8

704e90417b31be…051b62aa69409f

1 in → 2 out5.6726 XPM227 B

ANg9zRa3…R25oMmFX AUcQ7tLk…NRpHt1Sd

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.

1.827 × 10⁹⁶(97-digit number)

18278200644610991746…79423931469807105999

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

1.827 × 10⁹⁶(97-digit number)

18278200644610991746…79423931469807105999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.827 × 10⁹⁶(97-digit number)

18278200644610991746…79423931469807106001

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

3.655 × 10⁹⁶(97-digit number)

36556401289221983493…58847862939614211999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.655 × 10⁹⁶(97-digit number)

36556401289221983493…58847862939614212001

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

7.311 × 10⁹⁶(97-digit number)

73112802578443966986…17695725879228423999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.311 × 10⁹⁶(97-digit number)

73112802578443966986…17695725879228424001

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

1.462 × 10⁹⁷(98-digit number)

14622560515688793397…35391451758456847999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.462 × 10⁹⁷(98-digit number)

14622560515688793397…35391451758456848001

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

2.924 × 10⁹⁷(98-digit number)

29245121031377586794…70782903516913695999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.924 × 10⁹⁷(98-digit number)

29245121031377586794…70782903516913696001

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 #619,735

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