Block #607,357

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 6/29/2014, 11:07:55 PM · Difficulty 10.9072 · 6,206,942 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

0fdcd964b8889471f60a2dd7691bf4c21849bc01fd95f03a1e3b3283235803c4

View on Chainz ↗

Height

#607,357

Difficulty

10.907178

Transactions

Size

1.56 KB

Version

Bits

0ae83cd8

Nonce

949,202,760

Timestamp

6/29/2014, 11:07:55 PM

Confirmations

6,206,942

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

b14824ad9e50af655cae24ab884c7a2501b14e3cf9f54165a27011b85226cf6e

Transactions (4)

Coinbase5f961d6a219496…e7c5955750243d

1 in → 1 out8.4200 XPM116 B

ANSXnLY2…Sd25TjkD

f954e360bf2971…f4b0851a5f1f4a

6 in → 1 out5.9997 XPM934 B

Aad1ALCx…p3Xya5NE

924821c01c09c3…e3d916003edaf5

1 in → 2 out6.6746 XPM226 B

ARGaBKu1…nMc1n15H AGXqJki6…YNiMZGMN

fdce33447dee6a…ffeb533343d6f1

1 in → 2 out4.3276 XPM227 B

AXGB59d7…cchBWKXz Ab8NMybc…BoCkUvHm

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.

1.543 × 10⁹⁸(99-digit number)

15439363863417813968…11621256261487198399

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

1.543 × 10⁹⁸(99-digit number)

15439363863417813968…11621256261487198399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.543 × 10⁹⁸(99-digit number)

15439363863417813968…11621256261487198401

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

3.087 × 10⁹⁸(99-digit number)

30878727726835627937…23242512522974396799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.087 × 10⁹⁸(99-digit number)

30878727726835627937…23242512522974396801

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

6.175 × 10⁹⁸(99-digit number)

61757455453671255874…46485025045948793599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.175 × 10⁹⁸(99-digit number)

61757455453671255874…46485025045948793601

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

1.235 × 10⁹⁹(100-digit number)

12351491090734251174…92970050091897587199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.235 × 10⁹⁹(100-digit number)

12351491090734251174…92970050091897587201

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

2.470 × 10⁹⁹(100-digit number)

24702982181468502349…85940100183795174399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.470 × 10⁹⁹(100-digit number)

24702982181468502349…85940100183795174401

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 #607,357

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