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Block #1,527,080

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 4/5/2016, 5:36:54 AM Β· Difficulty 10.6061 Β· 5,306,874 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
f141eff86235a5c73359c6965767bd750961bb4e048b306fa09009b0aa245ad7
View on Chainz β†—

Height

#1,527,080

Difficulty

10.606112

Transactions

1

Size

199 B

Version

2

Bits

0a9b2a25

Nonce

918,070,027

Timestamp

4/5/2016, 5:36:54 AM

Confirmations

5,306,874

Mined by

⛏️ P2SHARAEUZAthcwpXw5rN1fm8zvrJuNX5uXbvQ

Merkle Root

03d806e33d82dcb8a8694fae82c12fa110b5831a44ca907a0ee4ded91c687e7b
Transactions (1)
Coinbase03d806e33d82dc…e4ded91c687e7b
1 in β†’ 1 out8.8800 XPM109 B
ARAEUZAt…NX5uXbvQ
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.

2.473 Γ— 10⁹⁡(96-digit number)
24731609031903161990…27569079212682977279
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
2.473 Γ— 10⁹⁡(96-digit number)
24731609031903161990…27569079212682977279
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.473 Γ— 10⁹⁡(96-digit number)
24731609031903161990…27569079212682977281
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
4.946 Γ— 10⁹⁡(96-digit number)
49463218063806323981…55138158425365954559
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.946 Γ— 10⁹⁡(96-digit number)
49463218063806323981…55138158425365954561
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
9.892 Γ— 10⁹⁡(96-digit number)
98926436127612647963…10276316850731909119
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
9.892 Γ— 10⁹⁡(96-digit number)
98926436127612647963…10276316850731909121
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
1.978 Γ— 10⁹⁢(97-digit number)
19785287225522529592…20552633701463818239
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.978 Γ— 10⁹⁢(97-digit number)
19785287225522529592…20552633701463818241
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
3.957 Γ— 10⁹⁢(97-digit number)
39570574451045059185…41105267402927636479
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.957 Γ— 10⁹⁢(97-digit number)
39570574451045059185…41105267402927636481
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
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