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Block #936,270

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 2/14/2015, 3:30:19 PM Β· Difficulty 10.9015 Β· 5,890,881 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
3242ae2fd5d468add5fd28dc897f4c114030790efbe77cba6d1b8bb71bb36a0a
View on Chainz β†—

Height

#936,270

Difficulty

10.901484

Transactions

1

Size

208 B

Version

2

Bits

0ae6c7a1

Nonce

538,123,867

Timestamp

2/14/2015, 3:30:19 PM

Confirmations

5,890,881

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

9619af5fd92ccb80bc2ede995dfa23f5c5de1ac94856624468ab8a137391fd66
Transactions (1)
Coinbase9619af5fd92ccb…ab8a137391fd66
1 in β†’ 1 out8.4000 XPM116 B
ANSXnLY2…Sd25TjkD
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.

1.459 Γ— 10¹⁰⁰(101-digit number)
14590035450658496889…67196191528969830399
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
1.459 Γ— 10¹⁰⁰(101-digit number)
14590035450658496889…67196191528969830399
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.459 Γ— 10¹⁰⁰(101-digit number)
14590035450658496889…67196191528969830401
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
2.918 Γ— 10¹⁰⁰(101-digit number)
29180070901316993779…34392383057939660799
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.918 Γ— 10¹⁰⁰(101-digit number)
29180070901316993779…34392383057939660801
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
5.836 Γ— 10¹⁰⁰(101-digit number)
58360141802633987558…68784766115879321599
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
5.836 Γ— 10¹⁰⁰(101-digit number)
58360141802633987558…68784766115879321601
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
1.167 Γ— 10¹⁰¹(102-digit number)
11672028360526797511…37569532231758643199
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.167 Γ— 10¹⁰¹(102-digit number)
11672028360526797511…37569532231758643201
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
2.334 Γ— 10¹⁰¹(102-digit number)
23344056721053595023…75139064463517286399
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.334 Γ— 10¹⁰¹(102-digit number)
23344056721053595023…75139064463517286401
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
4.668 Γ— 10¹⁰¹(102-digit number)
46688113442107190046…50278128927034572799
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:57,861,392 XPMΒ·at block #6,827,150 Β· updates every 60s
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