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Block #1,341,509

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 11/25/2015, 7:34:40 PM Β· Difficulty 10.8040 Β· 5,476,471 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
78c62d5baa9cb8ad73f235491cdd26ea5ffb2f287d2c8472f666c206d5bec382
View on Chainz β†—

Height

#1,341,509

Difficulty

10.803997

Transactions

2

Size

15.89 KB

Version

2

Bits

0acdd2bc

Nonce

97,660,734

Timestamp

11/25/2015, 7:34:40 PM

Confirmations

5,476,471

Mined by

⛏️ P2SHAS5j2wcSBnGy7nd4oPqQq3fDWy1daq5Rjt

Merkle Root

aff0fb13c84992fca0c2e982c28492339b3af2b763ad7741e50898b03c5b2a81
Transactions (2)
Coinbase6b78a2b606fb79…353b2c3ca488b7
1 in β†’ 1 out8.7900 XPM109 B
AS5j2wcS…1daq5Rjt
037fca8cf116f2…881a46b605bccd
108 in β†’ 2 out497.5000 XPM15.70 KB
AbzdMQ4H…wBeaixsNAa6e6Sys…wXYUy8ks
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.

3.266 Γ— 10⁹⁷(98-digit number)
32664653993310787399…16497242910156390399
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
3.266 Γ— 10⁹⁷(98-digit number)
32664653993310787399…16497242910156390399
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.266 Γ— 10⁹⁷(98-digit number)
32664653993310787399…16497242910156390401
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
6.532 Γ— 10⁹⁷(98-digit number)
65329307986621574798…32994485820312780799
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
6.532 Γ— 10⁹⁷(98-digit number)
65329307986621574798…32994485820312780801
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
1.306 Γ— 10⁹⁸(99-digit number)
13065861597324314959…65988971640625561599
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.306 Γ— 10⁹⁸(99-digit number)
13065861597324314959…65988971640625561601
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
2.613 Γ— 10⁹⁸(99-digit number)
26131723194648629919…31977943281251123199
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.613 Γ— 10⁹⁸(99-digit number)
26131723194648629919…31977943281251123201
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
5.226 Γ— 10⁹⁸(99-digit number)
52263446389297259838…63955886562502246399
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
5.226 Γ— 10⁹⁸(99-digit number)
52263446389297259838…63955886562502246401
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:57,787,910 XPMΒ·at block #6,817,979 Β· updates every 60s
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