Block #1,356,455

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 12/5/2015, 9:39:09 PM · Difficulty 10.8203 · 5,439,389 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

b99b51109ae3b5191b6f511d0f1846b6158f60e912c43a8dd4afe775bea6e7b9

View on Chainz ↗

Height

#1,356,455

Difficulty

10.820317

Transactions

Size

5.14 KB

Version

Bits

0ad20051

Nonce

757,534,337

Timestamp

12/5/2015, 9:39:09 PM

Confirmations

5,439,389

Mined by

⛏️ P2SHAX4wr5vhZwqEgAV6cP1s1efDGMvXQ21Ljg

Merkle Root

b5bbd76ec59d81e9d44ade2eb75e4bc1a9e6479e09b0ef5c3696faf08928418b

Transactions (4)

Coinbasea7ba133a927fa7…2c17adb94144ba

1 in → 1 out8.5900 XPM110 B

AX4wr5vh…vXQ21Ljg

2f69719e2f69ba…398451db200b9d

1 in → 33 out92.4117 XPM1.25 KB

AUPrvtBQ…eDZNqhMQ AKbxwoAi…3YJdUVER APYK5tFc…c3k4g6mn AYyL66c1…m9CXqx5f AXcJuq3j…jZRbSks3

f21628e423d4bf…f241f77e8bb608

1 in → 51 out62.4929 XPM1.85 KB

AFtHvw9h…LWs2dyQ5 AQkdgVgz…bKpy7x8q AKZsRszs…NbdDzV3V AXmeB4pu…zVTzUiGF ARp2r22t…wbBidUh3

ff9831924a8725…fc611f6399902f

1 in → 51 out3.9800 XPM1.85 KB

ASCVSbVk…rPaegyxe AH4dET7t…P59jz82N AZ5GiScw…a6QkRRwT AMfPEFty…MoiGTaKf AbdJT9zW…SXepdTCC

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.

2.800 × 10⁹⁶(97-digit number)

28001984204491596776…38190449237741076479

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

2.800 × 10⁹⁶(97-digit number)

28001984204491596776…38190449237741076479

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.800 × 10⁹⁶(97-digit number)

28001984204491596776…38190449237741076481

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

5.600 × 10⁹⁶(97-digit number)

56003968408983193553…76380898475482152959

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.600 × 10⁹⁶(97-digit number)

56003968408983193553…76380898475482152961

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

1.120 × 10⁹⁷(98-digit number)

11200793681796638710…52761796950964305919

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.120 × 10⁹⁷(98-digit number)

11200793681796638710…52761796950964305921

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

2.240 × 10⁹⁷(98-digit number)

22401587363593277421…05523593901928611839

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.240 × 10⁹⁷(98-digit number)

22401587363593277421…05523593901928611841

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

4.480 × 10⁹⁷(98-digit number)

44803174727186554842…11047187803857223679

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.480 × 10⁹⁷(98-digit number)

44803174727186554842…11047187803857223681

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

8.960 × 10⁹⁷(98-digit number)

89606349454373109685…22094375607714447359

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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