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Block #12,339

TWNLength 8β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/11/2013, 9:39:15 AM Β· Difficulty 7.7564 Β· 6,793,715 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
0fcf35a2f1efc0b8367e7e506bb4601aeb2be4b37dc2e9501721c3c2c643d074
View on Chainz β†—

Height

#12,339

Difficulty

7.756401

Transactions

1

Size

197 B

Version

2

Bits

07c1a37b

Nonce

151

Timestamp

7/11/2013, 9:39:15 AM

Confirmations

6,793,715

Mined by

⛏️ P2SHAM6VRLKvWNLUn43QLb3EuhPjXzByN91i1u

Merkle Root

0942a0098b19628a67bc9288007502adb5a223781f6f90282d9ca91b2658ad46
Transactions (1)
Coinbase0942a0098b1962…9ca91b2658ad46
1 in β†’ 1 out16.6000 XPM108 B
AM6VRLKv…ByN91i1u
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.

5.726 Γ— 10⁹¹(92-digit number)
57263401208372647708…47216310854165581039
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
5.726 Γ— 10⁹¹(92-digit number)
57263401208372647708…47216310854165581039
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
5.726 Γ— 10⁹¹(92-digit number)
57263401208372647708…47216310854165581041
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
1.145 Γ— 10⁹²(93-digit number)
11452680241674529541…94432621708331162079
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.145 Γ— 10⁹²(93-digit number)
11452680241674529541…94432621708331162081
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
2.290 Γ— 10⁹²(93-digit number)
22905360483349059083…88865243416662324159
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.290 Γ— 10⁹²(93-digit number)
22905360483349059083…88865243416662324161
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
4.581 Γ— 10⁹²(93-digit number)
45810720966698118166…77730486833324648319
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.581 Γ— 10⁹²(93-digit number)
45810720966698118166…77730486833324648321
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^3 Γ— origin + 1 βˆ’ 2^3 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 8 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
CommonChain length 8

Found in most blocks. The baseline for Primecoin's proof-of-work.

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:57,692,515 XPMΒ·at block #6,806,053 Β· updates every 60s
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