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Block #2,056,321

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 4/5/2017, 7:36:24 AM Β· Difficulty 10.8196 Β· 4,777,573 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
3198946ee71bff09eb0a1ec5ceab3ab1f04f8707c49d818e7d8f39a5b10bc591
View on Chainz β†—

Height

#2,056,321

Difficulty

10.819575

Transactions

2

Size

1.14 KB

Version

2

Bits

0ad1cfb2

Nonce

795,432,467

Timestamp

4/5/2017, 7:36:24 AM

Confirmations

4,777,573

Mined by

⛏️ P2SHAcYpCvdaBBNg3oKjr7SfuvhZwKVMv6QvZW

Merkle Root

e7f2049bdf24edc7023ed25c9370d6226d31927f9dc18e70fdc32c62aa39aad3
Transactions (2)
Coinbased04f2c054bc514…a600be8704d77b
1 in β†’ 1 out8.5400 XPM110 B
AcYpCvda…VMv6QvZW
2e5740cb82fbe3…4128ace5933b6d
6 in β†’ 2 out49.5943 XPM966 B
Ab7uG9ff…yHFA4Ev4APrSaX9c…vkTNdxaC
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.

7.541 Γ— 10⁹⁴(95-digit number)
75412244291915464664…66694257123225091199
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
7.541 Γ— 10⁹⁴(95-digit number)
75412244291915464664…66694257123225091199
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
7.541 Γ— 10⁹⁴(95-digit number)
75412244291915464664…66694257123225091201
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
1.508 Γ— 10⁹⁡(96-digit number)
15082448858383092932…33388514246450182399
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.508 Γ— 10⁹⁡(96-digit number)
15082448858383092932…33388514246450182401
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
3.016 Γ— 10⁹⁡(96-digit number)
30164897716766185865…66777028492900364799
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.016 Γ— 10⁹⁡(96-digit number)
30164897716766185865…66777028492900364801
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
6.032 Γ— 10⁹⁡(96-digit number)
60329795433532371731…33554056985800729599
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
6.032 Γ— 10⁹⁡(96-digit number)
60329795433532371731…33554056985800729601
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
1.206 Γ— 10⁹⁢(97-digit number)
12065959086706474346…67108113971601459199
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.206 Γ— 10⁹⁢(97-digit number)
12065959086706474346…67108113971601459201
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
2.413 Γ— 10⁹⁢(97-digit number)
24131918173412948692…34216227943202918399
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
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