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Block #2,125,432

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 5/20/2017, 1:50:53 PM Β· Difficulty 10.9188 Β· 4,707,998 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
aaf3442e4ed8154b352b01f1e4cac3d51ff018ad15c246819f372dab1ae61304
View on Chainz β†—

Height

#2,125,432

Difficulty

10.918842

Transactions

2

Size

426 B

Version

2

Bits

0aeb3938

Nonce

117,543,821

Timestamp

5/20/2017, 1:50:53 PM

Confirmations

4,707,998

Mined by

⛏️ P2SHASwAGG3LwEA3rUuUQsEvtQiuBgud9qxgJg

Merkle Root

520ced9451b9fd23fdfea794731d96b6ef2e2e362b88e8afb6f31d53235229df
Transactions (2)
Coinbasefdd5d1929f74fb…3abc40bf529806
1 in β†’ 1 out8.3800 XPM110 B
ASwAGG3L…ud9qxgJg
b3aceb35ed0854…653a5c94a359ce
1 in β†’ 2 out304726.0481 XPM226 B
AbwvSqcK…sm5soskiATNNwPCV…id21vw5x
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.

2.929 Γ— 10⁹³(94-digit number)
29295118908355833988…42948222849264513179
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
2.929 Γ— 10⁹³(94-digit number)
29295118908355833988…42948222849264513179
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.929 Γ— 10⁹³(94-digit number)
29295118908355833988…42948222849264513181
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
5.859 Γ— 10⁹³(94-digit number)
58590237816711667977…85896445698529026359
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.859 Γ— 10⁹³(94-digit number)
58590237816711667977…85896445698529026361
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
1.171 Γ— 10⁹⁴(95-digit number)
11718047563342333595…71792891397058052719
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.171 Γ— 10⁹⁴(95-digit number)
11718047563342333595…71792891397058052721
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
2.343 Γ— 10⁹⁴(95-digit number)
23436095126684667191…43585782794116105439
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.343 Γ— 10⁹⁴(95-digit number)
23436095126684667191…43585782794116105441
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
4.687 Γ— 10⁹⁴(95-digit number)
46872190253369334382…87171565588232210879
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.687 Γ— 10⁹⁴(95-digit number)
46872190253369334382…87171565588232210881
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
9.374 Γ— 10⁹⁴(95-digit number)
93744380506738668764…74343131176464421759
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:57,911,645 XPMΒ·at block #6,833,429 Β· updates every 60s
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