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Block #876,276

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 12/31/2014, 6:11:17 AM Β· Difficulty 10.9649 Β· 5,948,550 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
8d751bd3b150d384456878fbbed0c956f7507ce2f4e3d4ac08fe90e8951706cc
View on Chainz β†—

Height

#876,276

Difficulty

10.964878

Transactions

2

Size

6.05 KB

Version

2

Bits

0af70247

Nonce

646,164,069

Timestamp

12/31/2014, 6:11:17 AM

Confirmations

5,948,550

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

292d0bd05ba96a046d58e56cadb6b58a6795c936b6796d8b7d9d306a8f4a572a
Transactions (2)
Coinbasecbaef7528c0e39…355e2c6e599688
1 in β†’ 1 out8.3600 XPM116 B
ANSXnLY2…Sd25TjkD
3154810a4c7a1e…5892121ead2ad9
40 in β†’ 2 out500.0126 XPM5.85 KB
AJjnK9uC…VreFquR4AHNHh8yu…gMW9rtoz
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) β€” it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

3.771 Γ— 10⁹⁡(96-digit number)
37719225063561736124…48734358021453282179
Discovered Prime Numbers
Lower: 2^k Γ— origin βˆ’ 1 | Upper: 2^k Γ— 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 β€” Twin Prime Pair (origin Β± 1)
origin βˆ’ 1
3.771 Γ— 10⁹⁡(96-digit number)
37719225063561736124…48734358021453282179
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.771 Γ— 10⁹⁡(96-digit number)
37719225063561736124…48734358021453282181
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: origin + 1 βˆ’ origin βˆ’ 1 = 2 (twin primes βœ“)
Level 1 β€” Twin Prime Pair (2^1 Γ— origin Β± 1)
2^1 Γ— origin βˆ’ 1
7.543 Γ— 10⁹⁡(96-digit number)
75438450127123472249…97468716042906564359
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
7.543 Γ— 10⁹⁡(96-digit number)
75438450127123472249…97468716042906564361
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^1 Γ— origin + 1 βˆ’ 2^1 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 2 β€” Twin Prime Pair (2^2 Γ— origin Β± 1)
2^2 Γ— origin βˆ’ 1
1.508 Γ— 10⁹⁢(97-digit number)
15087690025424694449…94937432085813128719
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.508 Γ— 10⁹⁢(97-digit number)
15087690025424694449…94937432085813128721
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^2 Γ— origin + 1 βˆ’ 2^2 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 3 β€” Twin Prime Pair (2^3 Γ— origin Β± 1)
2^3 Γ— origin βˆ’ 1
3.017 Γ— 10⁹⁢(97-digit number)
30175380050849388899…89874864171626257439
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.017 Γ— 10⁹⁢(97-digit number)
30175380050849388899…89874864171626257441
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^3 Γ— origin + 1 βˆ’ 2^3 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 4 β€” Twin Prime Pair (2^4 Γ— origin Β± 1)
2^4 Γ— origin βˆ’ 1
6.035 Γ— 10⁹⁢(97-digit number)
60350760101698777799…79749728343252514879
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
6.035 Γ— 10⁹⁢(97-digit number)
60350760101698777799…79749728343252514881
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 5 β€” Twin Prime Pair (2^5 Γ— origin Β± 1)
2^5 Γ— origin βˆ’ 1
1.207 Γ— 10⁹⁷(98-digit number)
12070152020339755559…59499456686505029759
Verify on FactorDB β†—Wolfram Alpha β†—

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 β€” the large number shown above β€” anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

β˜…β˜…β˜…β˜†β˜†
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 Γ— 3 Γ— 5 Γ— 7 Γ— …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial β€” that divisibility is part of the proof.

Prime Chain Origin = First Prime Γ— Primorial (2Β·3Β·5Β·7Β·11·…)
Source: Primecoin prime.cpp β€” CheckPrimeProofOfWork()

This is why the origin has many small prime factors β€” 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 βˆ’ 1 and p+2 = origin/primorial + 1
Cross-reference on Chainz Explorer
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