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Block #1,115,228

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 6/18/2015, 8:27:49 AM Β· Difficulty 10.9192 Β· 5,699,625 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
2e048a2ff9cec23a5ee752a9ae227f759f866858519235c157b9e1dd3c407b28
View on Chainz β†—

Height

#1,115,228

Difficulty

10.919247

Transactions

2

Size

1.86 KB

Version

2

Bits

0aeb53bf

Nonce

1,141,806,791

Timestamp

6/18/2015, 8:27:49 AM

Confirmations

5,699,625

Mined by

⛏️ P2SHAPUnwe2pDXYEuExjL3rWQqvg4yy9nUhw4Q

Merkle Root

d72ec3e47790dfb751c113525734af379fff30a2482c368cb8bbdbf7847a129f
Transactions (2)
Coinbase9651bbcdcd05bf…d9adcab9043f6c
1 in β†’ 1 out8.3900 XPM110 B
APUnwe2p…y9nUhw4Q
c630233376608d…bf2b077cd748f5
11 in β†’ 2 out1187.0108 XPM1.66 KB
AXGT53FV…Z73LLTKZAWMqNayR…CMSsDUnt
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.

9.341 Γ— 10⁹⁴(95-digit number)
93419832557443811186…23865375838947425279
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
9.341 Γ— 10⁹⁴(95-digit number)
93419832557443811186…23865375838947425279
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
9.341 Γ— 10⁹⁴(95-digit number)
93419832557443811186…23865375838947425281
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
1.868 Γ— 10⁹⁡(96-digit number)
18683966511488762237…47730751677894850559
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.868 Γ— 10⁹⁡(96-digit number)
18683966511488762237…47730751677894850561
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
3.736 Γ— 10⁹⁡(96-digit number)
37367933022977524474…95461503355789701119
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.736 Γ— 10⁹⁡(96-digit number)
37367933022977524474…95461503355789701121
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
7.473 Γ— 10⁹⁡(96-digit number)
74735866045955048949…90923006711579402239
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
7.473 Γ— 10⁹⁡(96-digit number)
74735866045955048949…90923006711579402241
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
1.494 Γ— 10⁹⁢(97-digit number)
14947173209191009789…81846013423158804479
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.494 Γ— 10⁹⁢(97-digit number)
14947173209191009789…81846013423158804481
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
2.989 Γ— 10⁹⁢(97-digit number)
29894346418382019579…63692026846317608959
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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