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Block #1,534,533

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 4/10/2016, 7:37:46 AM Β· Difficulty 10.6169 Β· 5,292,189 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
37d2fbcca17955b8d9344ca9ef32828ef4fa03a6ce774fa57eec9028d01f8036
View on Chainz β†—

Height

#1,534,533

Difficulty

10.616921

Transactions

2

Size

7.61 KB

Version

2

Bits

0a9dee85

Nonce

1,788,368,427

Timestamp

4/10/2016, 7:37:46 AM

Confirmations

5,292,189

Mined by

⛏️ P2SHAHXegyeixUaoRCk38mCPmWnU3ELjB7auGg

Merkle Root

640c43a39bd4dbbbc65ab33868d9a681fd055dc7ad48eb3f5e8fa3bd8b568d14
Transactions (2)
Coinbase1c5bc7b915d0fd…d280cf7252a255
1 in β†’ 1 out8.9400 XPM109 B
AHXegyei…LjB7auGg
a06ebfb9b851cb…0f3fa2a62d4741
51 in β†’ 1 out2820.5492 XPM7.42 KB
Aa8V4h1q…eF9C94L4
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.

3.715 Γ— 10⁹⁢(97-digit number)
37153115936023727577…36094121436377128959
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
3.715 Γ— 10⁹⁢(97-digit number)
37153115936023727577…36094121436377128959
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.715 Γ— 10⁹⁢(97-digit number)
37153115936023727577…36094121436377128961
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
7.430 Γ— 10⁹⁢(97-digit number)
74306231872047455154…72188242872754257919
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
7.430 Γ— 10⁹⁢(97-digit number)
74306231872047455154…72188242872754257921
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
1.486 Γ— 10⁹⁷(98-digit number)
14861246374409491030…44376485745508515839
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.486 Γ— 10⁹⁷(98-digit number)
14861246374409491030…44376485745508515841
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
2.972 Γ— 10⁹⁷(98-digit number)
29722492748818982061…88752971491017031679
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.972 Γ— 10⁹⁷(98-digit number)
29722492748818982061…88752971491017031681
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
5.944 Γ— 10⁹⁷(98-digit number)
59444985497637964123…77505942982034063359
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
5.944 Γ— 10⁹⁷(98-digit number)
59444985497637964123…77505942982034063361
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:57,857,930 XPMΒ·at block #6,826,721 Β· updates every 60s
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