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Block #1,171,081

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 7/26/2015, 9:14:13 AM Β· Difficulty 10.9366 Β· 5,670,825 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
727c9b364b2a6f6918215b4a643cae51353fccd25f868ef10270c7014efc7279
View on Chainz β†—

Height

#1,171,081

Difficulty

10.936639

Transactions

1

Size

199 B

Version

2

Bits

0aefc79b

Nonce

140,757,522

Timestamp

7/26/2015, 9:14:13 AM

Confirmations

5,670,825

Mined by

⛏️ P2SHAHijza9YE1P3Cb6UfcD21Tud8oDBVLvwt2

Merkle Root

9edbf967a4a3fab3fe1c4eb0d6095061750b06be09e073f10ca2663585e94870
Transactions (1)
Coinbase9edbf967a4a3fa…a2663585e94870
1 in β†’ 1 out8.3500 XPM110 B
AHijza9Y…DBVLvwt2
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.

8.423 Γ— 10⁹²(93-digit number)
84233618767736358780…60125047110957972479
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
8.423 Γ— 10⁹²(93-digit number)
84233618767736358780…60125047110957972479
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
8.423 Γ— 10⁹²(93-digit number)
84233618767736358780…60125047110957972481
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
1.684 Γ— 10⁹³(94-digit number)
16846723753547271756…20250094221915944959
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.684 Γ— 10⁹³(94-digit number)
16846723753547271756…20250094221915944961
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
3.369 Γ— 10⁹³(94-digit number)
33693447507094543512…40500188443831889919
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.369 Γ— 10⁹³(94-digit number)
33693447507094543512…40500188443831889921
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
6.738 Γ— 10⁹³(94-digit number)
67386895014189087024…81000376887663779839
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
6.738 Γ— 10⁹³(94-digit number)
67386895014189087024…81000376887663779841
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
1.347 Γ— 10⁹⁴(95-digit number)
13477379002837817404…62000753775327559679
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.347 Γ— 10⁹⁴(95-digit number)
13477379002837817404…62000753775327559681
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
2.695 Γ— 10⁹⁴(95-digit number)
26954758005675634809…24001507550655119359
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
Circulating Supply:57,979,622 XPMΒ·at block #6,841,905 Β· updates every 60s
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