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Block #1,371,775

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 12/16/2015, 5:45:06 PM Β· Difficulty 10.8106 Β· 5,472,300 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
d143803431194ebe7b5418f033c62b1c17a295074562f9ff59020eba7fd92118
View on Chainz β†—

Height

#1,371,775

Difficulty

10.810602

Transactions

1

Size

200 B

Version

2

Bits

0acf839d

Nonce

681,715,760

Timestamp

12/16/2015, 5:45:06 PM

Confirmations

5,472,300

Mined by

⛏️ P2SHAVJXWhimCgzNDwEF3GfDxjianDcBBeq19m

Merkle Root

bb146b354db22d081765f3758085f73d87471795707e4d18acc9f0219b5f97d5
Transactions (1)
Coinbasebb146b354db22d…c9f0219b5f97d5
1 in β†’ 1 out8.5400 XPM110 B
AVJXWhim…cBBeq19m
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.

8.441 Γ— 10⁹⁴(95-digit number)
84416418832000127337…52368947112152131599
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
8.441 Γ— 10⁹⁴(95-digit number)
84416418832000127337…52368947112152131599
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
8.441 Γ— 10⁹⁴(95-digit number)
84416418832000127337…52368947112152131601
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
1.688 Γ— 10⁹⁡(96-digit number)
16883283766400025467…04737894224304263199
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.688 Γ— 10⁹⁡(96-digit number)
16883283766400025467…04737894224304263201
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
3.376 Γ— 10⁹⁡(96-digit number)
33766567532800050934…09475788448608526399
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.376 Γ— 10⁹⁡(96-digit number)
33766567532800050934…09475788448608526401
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
6.753 Γ— 10⁹⁡(96-digit number)
67533135065600101869…18951576897217052799
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
6.753 Γ— 10⁹⁡(96-digit number)
67533135065600101869…18951576897217052801
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
1.350 Γ— 10⁹⁢(97-digit number)
13506627013120020373…37903153794434105599
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.350 Γ— 10⁹⁢(97-digit number)
13506627013120020373…37903153794434105601
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:57,996,975 XPMΒ·at block #6,844,074 Β· updates every 60s
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