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Block #2,101,856

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 5/5/2017, 11:09:39 PM Β· Difficulty 10.8648 Β· 4,738,599 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
1302cb8edfd8c53492e71956c610d9b5f2d06437a8d8b5c473541b33476e210f
View on Chainz β†—

Height

#2,101,856

Difficulty

10.864798

Transactions

1

Size

201 B

Version

2

Bits

0add636f

Nonce

421,204,170

Timestamp

5/5/2017, 11:09:39 PM

Confirmations

4,738,599

Mined by

⛏️ P2SHAdnSdgokhQFteniU2n9xDaZwX5sgsjBrsP

Merkle Root

f39e2fe7121df37484a8aa651a760b43fea5b763527679f79d5dd28bef888ea6
Transactions (1)
Coinbasef39e2fe7121df3…5dd28bef888ea6
1 in β†’ 1 out8.4600 XPM110 B
AdnSdgok…sgsjBrsP
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.

4.286 Γ— 10⁹⁢(97-digit number)
42869009845470445326…37921110742501698559
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
4.286 Γ— 10⁹⁢(97-digit number)
42869009845470445326…37921110742501698559
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.286 Γ— 10⁹⁢(97-digit number)
42869009845470445326…37921110742501698561
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
8.573 Γ— 10⁹⁢(97-digit number)
85738019690940890652…75842221485003397119
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
8.573 Γ— 10⁹⁢(97-digit number)
85738019690940890652…75842221485003397121
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
1.714 Γ— 10⁹⁷(98-digit number)
17147603938188178130…51684442970006794239
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.714 Γ— 10⁹⁷(98-digit number)
17147603938188178130…51684442970006794241
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
3.429 Γ— 10⁹⁷(98-digit number)
34295207876376356261…03368885940013588479
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.429 Γ— 10⁹⁷(98-digit number)
34295207876376356261…03368885940013588481
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
6.859 Γ— 10⁹⁷(98-digit number)
68590415752752712522…06737771880027176959
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
6.859 Γ— 10⁹⁷(98-digit number)
68590415752752712522…06737771880027176961
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:57,967,971 XPMΒ·at block #6,840,454 Β· updates every 60s
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