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Block #1,478,069

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 3/1/2016, 3:14:34 AM Β· Difficulty 10.7076 Β· 5,365,651 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
406c1ead8b0ea187bf66e8a9050c8cca238ec49ca29130ca15e5c681ea7b5a84
View on Chainz β†—

Height

#1,478,069

Difficulty

10.707638

Transactions

1

Size

200 B

Version

2

Bits

0ab527cb

Nonce

600,620,679

Timestamp

3/1/2016, 3:14:34 AM

Confirmations

5,365,651

Mined by

⛏️ P2SHAPxdRoHamh5LfDfHfsEbZCcWHZQmxFTfMD

Merkle Root

76bbcde31fac8538eec31b6493f8d12c4d0ea4b0e35f7bea40f3e347065d6ace
Transactions (1)
Coinbase76bbcde31fac85…f3e347065d6ace
1 in β†’ 1 out8.7100 XPM110 B
APxdRoHa…QmxFTfMD
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.

2.508 Γ— 10⁹⁡(96-digit number)
25089919839223472632…25009135306386288959
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
2.508 Γ— 10⁹⁡(96-digit number)
25089919839223472632…25009135306386288959
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.508 Γ— 10⁹⁡(96-digit number)
25089919839223472632…25009135306386288961
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
5.017 Γ— 10⁹⁡(96-digit number)
50179839678446945264…50018270612772577919
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.017 Γ— 10⁹⁡(96-digit number)
50179839678446945264…50018270612772577921
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
1.003 Γ— 10⁹⁢(97-digit number)
10035967935689389052…00036541225545155839
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.003 Γ— 10⁹⁢(97-digit number)
10035967935689389052…00036541225545155841
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
2.007 Γ— 10⁹⁢(97-digit number)
20071935871378778105…00073082451090311679
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.007 Γ— 10⁹⁢(97-digit number)
20071935871378778105…00073082451090311681
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
4.014 Γ— 10⁹⁢(97-digit number)
40143871742757556211…00146164902180623359
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.014 Γ— 10⁹⁢(97-digit number)
40143871742757556211…00146164902180623361
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
8.028 Γ— 10⁹⁢(97-digit number)
80287743485515112423…00292329804361246719
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:57,994,130 XPMΒ·at block #6,843,719 Β· updates every 60s
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