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Block #1,534,748

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 4/10/2016, 10:57:46 AM Β· Difficulty 10.6182 Β· 5,281,543 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
823f0bbd855162e09b5154b7b249d544e25922e681c4d006e9692d59c092bc09
View on Chainz β†—

Height

#1,534,748

Difficulty

10.618215

Transactions

3

Size

15.03 KB

Version

2

Bits

0a9e4350

Nonce

203,809,245

Timestamp

4/10/2016, 10:57:46 AM

Confirmations

5,281,543

Mined by

⛏️ P2SHAYETsKLsq61oZ1Qz6bDDH7yduFD4P2Qkwc

Merkle Root

5d869e76d3f0d9021896a3bce2dcdc2415e85abbf11690ae6e25e33ab965bd48
Transactions (3)
Coinbase68cad7cfed6be3…e5acb6efd14c89
1 in β†’ 1 out9.0200 XPM109 B
AYETsKLs…D4P2Qkwc
c2712dd298db1a…0403bea9228e18
51 in β†’ 1 out3130.1754 XPM7.42 KB
AXYBxd8P…4EDxssqF
93c5b7e657c3bd…86b5cca08affa2
51 in β†’ 1 out1456.6294 XPM7.42 KB
AKjYmhGp…iYjiG9km
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.

1.434 Γ— 10⁹⁴(95-digit number)
14348411985753227646…28158409925904050959
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
1.434 Γ— 10⁹⁴(95-digit number)
14348411985753227646…28158409925904050959
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.434 Γ— 10⁹⁴(95-digit number)
14348411985753227646…28158409925904050961
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
2.869 Γ— 10⁹⁴(95-digit number)
28696823971506455292…56316819851808101919
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.869 Γ— 10⁹⁴(95-digit number)
28696823971506455292…56316819851808101921
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
5.739 Γ— 10⁹⁴(95-digit number)
57393647943012910584…12633639703616203839
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
5.739 Γ— 10⁹⁴(95-digit number)
57393647943012910584…12633639703616203841
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
1.147 Γ— 10⁹⁡(96-digit number)
11478729588602582116…25267279407232407679
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.147 Γ— 10⁹⁡(96-digit number)
11478729588602582116…25267279407232407681
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
2.295 Γ— 10⁹⁡(96-digit number)
22957459177205164233…50534558814464815359
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.295 Γ— 10⁹⁡(96-digit number)
22957459177205164233…50534558814464815361
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:57,774,445 XPMΒ·at block #6,816,290 Β· updates every 60s
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