Block #604,681

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 6/27/2014, 11:34:32 PM · Difficulty 10.9103 · 6,193,197 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

de0089a31bfd6060c88ed5d5d8689f8d49432948d703d5fcf6158db943f80e76

View on Chainz ↗

Height

#604,681

Difficulty

10.910260

Transactions

Size

1.41 KB

Version

Bits

0ae906cb

Nonce

234,628,478

Timestamp

6/27/2014, 11:34:32 PM

Confirmations

6,193,197

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

56a757e7f1e301928c359c463623ee92959d5efa9420fd546bfa47589d266d0f

Transactions (5)

Coinbase00f5e353b107f3…f26a6949c6d6cd

1 in → 1 out8.4300 XPM116 B

ANSXnLY2…Sd25TjkD

16f3264c584a7c…d3df6a34b9d86e

2 in → 4 out9.1181 XPM408 B

ALC1VQzr…2tnpfMyB AeKNrjNj…1NEq95Ta AH1wEe2R…srAfPtHd AUfa5LFJ…C4BhhWGa

b6abba918a02cd…5af1c24a022433

1 in → 2 out5.8584 XPM227 B

Ae7YXEyn…hnSYZsCr AZgHHtTe…q1hBJi1o

527567a016a179…42d7af0ece1356

1 in → 2 out4.2733 XPM226 B

ATJgzmre…e1pt2xQ5 AS9ZCvju…bu3NEFwZ

eb70a8ee5dd859…018adeac30bc4b

2 in → 2 out0.6327 XPM373 B

AdY5anxV…xLzTNv3y AK9166NA…jA3Boio5

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.

3.189 × 10¹⁰¹(102-digit number)

31890306447537453724…41912626872068341759

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

3.189 × 10¹⁰¹(102-digit number)

31890306447537453724…41912626872068341759

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.189 × 10¹⁰¹(102-digit number)

31890306447537453724…41912626872068341761

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

6.378 × 10¹⁰¹(102-digit number)

63780612895074907449…83825253744136683519

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.378 × 10¹⁰¹(102-digit number)

63780612895074907449…83825253744136683521

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

1.275 × 10¹⁰²(103-digit number)

12756122579014981489…67650507488273367039

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.275 × 10¹⁰²(103-digit number)

12756122579014981489…67650507488273367041

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

2.551 × 10¹⁰²(103-digit number)

25512245158029962979…35301014976546734079

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.551 × 10¹⁰²(103-digit number)

25512245158029962979…35301014976546734081

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

5.102 × 10¹⁰²(103-digit number)

51024490316059925959…70602029953093468159

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.102 × 10¹⁰²(103-digit number)

51024490316059925959…70602029953093468161

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