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Block #2,256,843

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 8/18/2017, 5:57:56 AM Β· Difficulty 10.9515 Β· 4,585,864 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
3f5bbce97ae90d4757bf1b45432566d217ed60fd4222b44452015defdd9cc027
View on Chainz β†—

Height

#2,256,843

Difficulty

10.951518

Transactions

1

Size

199 B

Version

2

Bits

0af396b6

Nonce

814,569,698

Timestamp

8/18/2017, 5:57:56 AM

Confirmations

4,585,864

Mined by

⛏️ P2SHAHCZokG1WpmrK8zBSd6bQBgdFYF4E6uAny

Merkle Root

945b1297b5efb8d505a147f6a81e44c97ac9e0181ccd8782ee85c730185469ae
Transactions (1)
Coinbase945b1297b5efb8…85c730185469ae
1 in β†’ 1 out8.3200 XPM110 B
AHCZokG1…F4E6uAny
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.

2.606 Γ— 10⁹³(94-digit number)
26069971872909963339…53993655674501314559
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
2.606 Γ— 10⁹³(94-digit number)
26069971872909963339…53993655674501314559
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.606 Γ— 10⁹³(94-digit number)
26069971872909963339…53993655674501314561
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
5.213 Γ— 10⁹³(94-digit number)
52139943745819926678…07987311349002629119
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.213 Γ— 10⁹³(94-digit number)
52139943745819926678…07987311349002629121
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
1.042 Γ— 10⁹⁴(95-digit number)
10427988749163985335…15974622698005258239
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.042 Γ— 10⁹⁴(95-digit number)
10427988749163985335…15974622698005258241
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
2.085 Γ— 10⁹⁴(95-digit number)
20855977498327970671…31949245396010516479
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.085 Γ— 10⁹⁴(95-digit number)
20855977498327970671…31949245396010516481
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
4.171 Γ— 10⁹⁴(95-digit number)
41711954996655941342…63898490792021032959
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.171 Γ— 10⁹⁴(95-digit number)
41711954996655941342…63898490792021032961
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

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 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
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 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:57,986,006 XPMΒ·at block #6,842,706 Β· updates every 60s
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