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Block #571,903

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 6/1/2014, 6:33:05 PM Β· Difficulty 10.9657 Β· 6,245,181 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
1117842d68eeaea3c6780f95343274f7d9e2ca94b26ad0618427f2f9b3e17c85
View on Chainz β†—

Height

#571,903

Difficulty

10.965698

Transactions

2

Size

2.16 KB

Version

2

Bits

0af73801

Nonce

654,987,044

Timestamp

6/1/2014, 6:33:05 PM

Confirmations

6,245,181

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

ec3158cd1c6e6fbc7f350a238f5fb70315f22d8ee76d2584df60ea70b691e186
Transactions (2)
Coinbasee34f3a881830dd…5c4df2704380ba
1 in β†’ 1 out8.3300 XPM116 B
ANSXnLY2…Sd25TjkD
a93b8d6e00b1e7…a1d8f0450a8713
13 in β†’ 2 out36.8613 XPM1.95 KB
AUSBp3Jw…VuWFwvWbAdNMony6…XCvRp5gG
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.

1.053 Γ— 10⁹⁷(98-digit number)
10537293283396098823…43233308425919443899
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
1.053 Γ— 10⁹⁷(98-digit number)
10537293283396098823…43233308425919443899
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.053 Γ— 10⁹⁷(98-digit number)
10537293283396098823…43233308425919443901
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
2.107 Γ— 10⁹⁷(98-digit number)
21074586566792197646…86466616851838887799
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.107 Γ— 10⁹⁷(98-digit number)
21074586566792197646…86466616851838887801
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
4.214 Γ— 10⁹⁷(98-digit number)
42149173133584395293…72933233703677775599
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.214 Γ— 10⁹⁷(98-digit number)
42149173133584395293…72933233703677775601
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
8.429 Γ— 10⁹⁷(98-digit number)
84298346267168790587…45866467407355551199
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
8.429 Γ— 10⁹⁷(98-digit number)
84298346267168790587…45866467407355551201
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
1.685 Γ— 10⁹⁸(99-digit number)
16859669253433758117…91732934814711102399
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.685 Γ— 10⁹⁸(99-digit number)
16859669253433758117…91732934814711102401
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
3.371 Γ— 10⁹⁸(99-digit number)
33719338506867516234…83465869629422204799
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:57,780,710 XPMΒ·at block #6,817,083 Β· updates every 60s
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