Block #1,461,078

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/17/2016, 8:37:35 AM · Difficulty 10.7784 · 5,363,749 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

061319bebd271fee55121274b4a4101fd073767c126baf3b7a4cff79b019708a

View on Chainz ↗

Height

#1,461,078

Difficulty

10.778367

Transactions

Size

4.03 KB

Version

Bits

0ac74316

Nonce

258,361,439

Timestamp

2/17/2016, 8:37:35 AM

Confirmations

5,363,749

Mined by

⛏️ P2SHAGfgFKcQt3gVFQXpRwDtazYtQ9AYKSpvXu

Merkle Root

5a93a828faa2297de11972568be428507cfa422be800e8a2f20921cce7f95f4b

Transactions (2)

Coinbase1bffc1fe503128…13bcdce231611b

1 in → 1 out8.6300 XPM109 B

AGfgFKcQ…AYKSpvXu

65e50e88483f36…00b05d049ec68e

26 in → 2 out252.6905 XPM3.83 KB

AQcjeddP…AoqhXrhG AKarXodx…wrRWifiy

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.

1.070 × 10⁹⁴(95-digit number)

10705873008185213166…53156108674813627659

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

1.070 × 10⁹⁴(95-digit number)

10705873008185213166…53156108674813627659

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.070 × 10⁹⁴(95-digit number)

10705873008185213166…53156108674813627661

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

2.141 × 10⁹⁴(95-digit number)

21411746016370426332…06312217349627255319

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.141 × 10⁹⁴(95-digit number)

21411746016370426332…06312217349627255321

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

4.282 × 10⁹⁴(95-digit number)

42823492032740852664…12624434699254510639

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.282 × 10⁹⁴(95-digit number)

42823492032740852664…12624434699254510641

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

8.564 × 10⁹⁴(95-digit number)

85646984065481705328…25248869398509021279

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.564 × 10⁹⁴(95-digit number)

85646984065481705328…25248869398509021281

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

1.712 × 10⁹⁵(96-digit number)

17129396813096341065…50497738797018042559

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.712 × 10⁹⁵(96-digit number)

17129396813096341065…50497738797018042561

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 #1,461,078

Cookie Preferences