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Block #1,477,917

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 3/1/2016, 1:06:37 AM Β· Difficulty 10.7062 Β· 5,365,507 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
3ae0b00c14c777e791e5a1e3281c6b8e141eb1a128a5268b5b6b6a7b0958023b
View on Chainz β†—

Height

#1,477,917

Difficulty

10.706150

Transactions

1

Size

243 B

Version

2

Bits

0ab4c646

Nonce

92,193,163

Timestamp

3/1/2016, 1:06:37 AM

Confirmations

5,365,507

Mined by

⛏️ P2SHAdwKJkgSub5gUckyBUnSUJCm23L2zsc2ej

Merkle Root

d2b8ff6cc1614f25a16c26833a143239beed766e4c40c35eec1968ce4c51a5f2
Transactions (1)
Coinbased2b8ff6cc1614f…1968ce4c51a5f2
1 in β†’ 2 out8.7100 XPM152 B
AdwKJkgS…L2zsc2ejALPu3s2c…EJXLjVFh
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.

8.026 Γ— 10⁹⁡(96-digit number)
80265045775108156924…71740041744460807839
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
8.026 Γ— 10⁹⁡(96-digit number)
80265045775108156924…71740041744460807839
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
8.026 Γ— 10⁹⁡(96-digit number)
80265045775108156924…71740041744460807841
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
1.605 Γ— 10⁹⁢(97-digit number)
16053009155021631384…43480083488921615679
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.605 Γ— 10⁹⁢(97-digit number)
16053009155021631384…43480083488921615681
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
3.210 Γ— 10⁹⁢(97-digit number)
32106018310043262769…86960166977843231359
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.210 Γ— 10⁹⁢(97-digit number)
32106018310043262769…86960166977843231361
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
6.421 Γ— 10⁹⁢(97-digit number)
64212036620086525539…73920333955686462719
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
6.421 Γ— 10⁹⁢(97-digit number)
64212036620086525539…73920333955686462721
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
1.284 Γ— 10⁹⁷(98-digit number)
12842407324017305107…47840667911372925439
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.284 Γ— 10⁹⁷(98-digit number)
12842407324017305107…47840667911372925441
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:57,991,761 XPMΒ·at block #6,843,423 Β· updates every 60s
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