Block #608,881

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 6/30/2014, 10:19:28 PM · Difficulty 10.9096 · 6,187,031 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

a6494364074e90938bf7c16e885a27b2a272bc9930037a3da4829a319df73330

View on Chainz ↗

Height

#608,881

Difficulty

10.909628

Transactions

Size

1.09 KB

Version

Bits

0ae8dd5e

Nonce

177,416,316

Timestamp

6/30/2014, 10:19:28 PM

Confirmations

6,187,031

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

b13d3a17a84280b9170f97bd9fc7e146968bd43ca3da6f32b29cbeaf25f121d6

Transactions (5)

Coinbaseab989831ab95d3…6a1d17976da0bf

1 in → 1 out8.4300 XPM116 B

ANSXnLY2…Sd25TjkD

01e4319955b97f…63786b981f5a6c

1 in → 2 out7.3151 XPM226 B

AGzX6zrq…2sUqUFQZ AUPMNZx2…tTtr4Jw4

45175e38db21bb…b3418db2e66af6

1 in → 2 out7.2848 XPM226 B

Ab3ZA77H…R7ktRp2N AXWLUv12…NPxS6XxQ

b0a1e8efd19bb7…d2c44be11a27e4

1 in → 2 out7.2685 XPM226 B

AGzUYrUS…WHCt33zq AYrwBKyU…1S6w2wRP

fe00373522511a…23c1e6ed4e628d

1 in → 2 out7.2461 XPM226 B

AXfi8bGW…nf2vb7cM ATUJFkEF…j71DTZhm

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.

1.025 × 10⁹⁹(100-digit number)

10251909637200949082…23796433156282812159

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

1.025 × 10⁹⁹(100-digit number)

10251909637200949082…23796433156282812159

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.025 × 10⁹⁹(100-digit number)

10251909637200949082…23796433156282812161

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

2.050 × 10⁹⁹(100-digit number)

20503819274401898165…47592866312565624319

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.050 × 10⁹⁹(100-digit number)

20503819274401898165…47592866312565624321

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

4.100 × 10⁹⁹(100-digit number)

41007638548803796331…95185732625131248639

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.100 × 10⁹⁹(100-digit number)

41007638548803796331…95185732625131248641

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

8.201 × 10⁹⁹(100-digit number)

82015277097607592663…90371465250262497279

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.201 × 10⁹⁹(100-digit number)

82015277097607592663…90371465250262497281

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

1.640 × 10¹⁰⁰(101-digit number)

16403055419521518532…80742930500524994559

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.640 × 10¹⁰⁰(101-digit number)

16403055419521518532…80742930500524994561

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